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In this work we show that it is possible to calculate the fractionalintegrals and derivatives of order $\alpha$ (using the Riemann-Liouvilleformulation) of power functions $\left( t-\ast\right) ^{\beta}$ with $\beta$being any real value, so long as one pays attention to the proper choosing ofthe lower and upper limits according to the original function's domain. We,therefore, obtain valid expressions that are described in terms of functionseries of the type $\left( t-\ast\right) ^{\pm\alpha+k}$ and we also show thatthey are related to the famous hypergeometric functions of theMathematical-Physics.

Analysis of the Fractional Integrodifferentiability of Power Functions and some Identities with Hypergeometric Functions